Select faces within two cuts/edges
If you have a cut in there, you should have separate Mesh Islands. 

Hovering your mouse over the island of choice and pressing L will select the Linked Faces. You can look in the Operator Panel for additional options that will limit the selection, like Seams, for instance.

Alternatively, select just one element and hit Ctrl + L to select the linked faces, regardless of where your mouse is at that moment.